Vector and covector invariants of Lie superalgebras
In the paper under review the author continues his research from his previous paper [\textit{A. N. Sergeev}, Funkts. Anal. Prilozh. 26, No. 3, 88-90 (1992; Zbl 0838.17036)]. Let \(\mathfrak g\) be a subsuperalgebra of the Lie superalgebra \({\mathfrak gl}(V)\) of a finite dimensional superspace \(V\) over \(\mathbb{C}\). By invariant theory of \(\mathfrak g\) the author means the study of \(\mathfrak g\)-invariants in \({\mathfrak A}_{k,l}^{p,q}=S(V^k\oplus\pi(V)^l\oplus V^{\ast p}\oplus \pi(V^{\ast})^q)\). This symmetric algebra is isomorphic to \(S(U\otimes V\oplus V^{\ast}\otimes W)\), where \(U\) and \(W\) are superspaces of dimensions \((k,l)\) and \((p,q)\), respectively. In his previous paper the author described the generators of the algebra of \(\mathfrak g\)-invariants for each series of classical superalgebras and their central extensions. The generators were given up to the action of polarization operators, i.e. up to multiplication with elements of universal enveloping algebras. Now, the author generalizes these results and announces sets of generators (in the usual sense, not taking into account the action of the polarization operators) for the superalgebras \(\text{sl}(V)\), \(\text{osp}(V)\) and \(\text{sp}(V)\).
scientific article; zbMATH DE number 1023831
scientific article